Hello Richard! Thank you for your question. I am a licensed computer professional with over ten years of experience, and I will be assisting you today.
I'm sorry about the issue. Are you able to play videos from other websites (except youtube.com website)? Please try the followings in order to fix this issue:
1. Please disconnect the power cord from your modem / router for a few minutes, then reconnect.
2. Search for Adobe flash player in spotlight, then uninstall it.
3. In Safari, click on the Safari menu on the top
, click EMPTY CACHE if available, then click Empty button
, click on Safari menu on the top again
, click on Reset Safari, then click Reset button
4. Download and reinstall Adobe Flash Player at the website below:
5. Check http://www.youtube.com/
If that does not work, please download and install Firefox software at the website below:
, then open Firefox, then go to the youtube.com website in Firefox, then see if you can play videos in Firefox.
If needed, restart the computer and check.
If there is still any issue, please click on the Reply to Expert tab below, and reply back to me, so I can help further as you need. Thank you very much.